http://en.wikipedia.org/wiki/File:Solar_Spectrum.png
If you look at this link it shows that atmospheric absorption modifies the spectrum (in the fine detail) of the incident Sunlight in addition to the effect of Raleigh scattering (the general trend). Absorption effects are more marked at non-optical frequencies, of course, with huge amounts of absorption of microwave frequencies by water vapour. Both effects on the optical bands would get more and more pronounced as the atmosphere gets thicker and thicker.
I have a feeling that, in a thicker atmosphere, the effects of absorption by some of the more dense but more rare molecules (which collect more in the bottom layers) would be more marked than at the present atmospheric thickness and pressure. This would produce proportionally more noticeable colouring.

I assume you are taking snow to be a good reflector of light at all wavelengths, producing what we would call 'white' with the Sun overhead. Our (brain) colour compensation circuits do a lot better than those in cameras and I have a feeling that we would very soon accept a modified version of this if we were to spend much time under a more dense atmosphere, in much the same way as we 'see' white things as white under tungsten and flourescent lights.